Analytical results for the entanglement dynamics of disjoint blocks in the XY spin chain

Abstract

The study of the dynamics of entanglement measures after a quench has become a very active area of research in the last two decades, motivated by the development of experimental techniques. However, exact results in this context are available in only very few cases. In this work, we present the proof of the quasiparticle picture for the dynamics of entanglement entropies for two disjoint blocks in the XY chain after a quantum quench. As a byproduct, we also prove the quasiparticle conjecture for the mutual information in that model. Our calculations generalize those presented in [M. Fagotti, P. Calabrese, Phys. Rev. A 78, 010306 (2008)] to the case where the correlation matrix is a block-Toeplitz matrix, and rely on the multidimensional stationary phase approximation in the scaling limit. We also test the quasiparticle predictions against exact numerical calculations, and find excellent agreement. In the case of three blocks, we show that the tripartite information vanishes when at least two blocks are adjacent.

23 pages, v2: minor modifications

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Cited by in corpus (9)

• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• Negative tripartite mutual information after quantum quenches in integrable systems
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• The Fate of Entanglement
• Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
• Entanglement in dual unitary quantum circuits with impurities
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials